| Well, it's a bit
late for Happy New Year for all you prop twisters out there
in Happy Vortex land, so a happy Easter to yo'all. Had a real
treat the other day. Driving down the Reid Highway in Perth,
I spied a beaut willy-willy dead in front, so open the windows
and swerve right into it. Dust and papers went everywhere,
the s--- coloured Gemini swayed and rocked, what a treat.
Even Rosemary got a kick out of it. If you care to imagine
a prop blade sticking up from the ground in to the centre
of the vortex, then you've got the picture of where thrust
comes from. But not everyone has.
With almost predictable regularity, I get guys
wanting to put props on their hang gliders so they can foot
launch off their driveways. Great idea, but really tough to
achieve. The favourite is to hang a ducted fan onto your derriere,
usually with an OS90DF or some such, and be an instant Spaceman
Spiff. But it just doesn't work that way, there are some laws
of Physics, that just won't let go. Gravity is one, Conservation
of Energy is another. Climbing flight requires work to be
done, and that work has to come from somewhere. This is true
of all flight, so why pick on hang gliders? Well, hang gliders
are at the very extreme of useable propellers. They need high
static thrust because the pilot can only run to about 10 MPH
with 135 Kg strapped to his butt . Then the climb speed is
only about 20MPH, with prop RPM anywhere from 2500 on up to
9000. This is a combination which guarantees low propulsive
efficiency. But why? Surely if you make some good airfoils
and put in the right twists, polish it up and paint the tips
red, the propeller will be sure to have high efficiency. Not
so. To a very high degree, the efficiency of a propeller is
not set by its design or fabrication, but by the conditions
under which it must operate. High RPM and low airspeed kill
propellers, not matter how gorgeous they are. So what are
the underlying-factors at work here, perhaps we can learn
something to improve Yo-Yo flight.
There are two interesting notions to consider.
Firstly, there is a mass of air that flows through
the propeller disc. This air can be thought of as a tube of
air, of which the prop disc is the cross-section. The tube
of air behind the prop disc is the propeller slipstream. The
tube has a surprising property.
The velocity of the air in the tube at any given
cross-section is nearly uniform. One would think that the
air pushed back directly at the blade would have high velocity,
while the air between the blades had none. But it is not so.
Certainly there is variation, but far less than you would
guess. The propeller airfoils influence the air a long way
from the surfaces: this means the gap between the blades.
Secondly, the velocity imparted to the slipstream
by the propeller depends on the width of the blades (the chord
of the airfoils, more precisely) . This velocity is also called
the induced downwash velocity. One may have thought that increasing
the chord would increase mass flow, as the wider blade belts
into more air: but this is not so. Now thrust works by increasing
the mass flow through the propeller disc.
Increasing diameter provides a greater mass
of air for the prop to act upon.
Increasing blade chord produces thrust by increasing slipstream
velocity.
However, this is an expensive way of getting more thrust.
The kinetic energy imparted to the slipstream goes with the
square of the extra induced velocity, but only in direct proportion
to an increase in mass acted upon. Hence increasing chord
is an inefficient way of generating more thrust. Further,
high RPM means that the propeller blade angles must be low
for low speed flight. For low angles, the engine torque is
working directly against the drag of the airfoils, an action
which does not produce thrust. Increasing blade angle lowers
the amount of torque required to overcome this drag: further,
at the higher angle, the engine torque is then working against
the airfoil lift component, an action that does produce thrust.
It is these considerations that lead to an ideal blade angle
of 45 degrees.
Hence the powered hang glider, with restricted
prop diameter and high RPM, is in quite a bit of trouble so
far as efficiency is concerned. The type of efficiency loss,
where diameter is limited and slipstream velocities are high,
is termed "induced efficiency". The loss due to low blade
angles and the airfoil drag is termed "profile efficiency".
The losses due to induced and profile losses are commonly
of the same size: one cannot be neglected in favour of the
other.
So for you hang glider buffs out there, in 1989
you need to look back to the Wright brothers: 12 HP, 400 RPM,
8' diameter, two propeller discs, and 25 MPH. Its all there.
End of sermon. |
